# Equivariant amortized inference of poses for cryo-EM

arXiv: https://arxiv.org/abs/2406.01630 · HTML: https://mlsanity.com/paper/2406.01630/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 15 of 15)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [Explorations in Homeomorphic Variational Auto-Encoding](https://mlsanity.com/paper/1807.04689/) (2018)
- [Explicitly disentangling image content from translation and rotation with spatial-VAE](https://mlsanity.com/paper/1909.11663/) (2019)
- [CryoAI: Amortized Inference of Poses for Ab Initio Reconstruction of 3D Molecular Volumes from Real Cryo-EM Images](https://mlsanity.com/paper/2203.08138/) (2022)
- [Amortized Inference for Heterogeneous Reconstruction in Cryo-EM](https://mlsanity.com/paper/2210.07387/) (2022)
- [Deep Generative Modeling for Volume Reconstruction in Cryo-Electron Microscopy](https://mlsanity.com/paper/2201.02867/) (2022)
- [Inferring a Continuous Distribution of Atom Coordinates from Cryo-EM Images using VAEs](https://mlsanity.com/paper/2106.14108/) (2021)
- [Estimation of Orientation and Camera Parameters from Cryo-Electron Microscopy Images with Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1911.08121/) (2019)
- [Unsupervised Object Representation Learning using Translation and Rotation Group Equivariant VAE](https://mlsanity.com/paper/2210.12918/) (2022)
- [Deep learning for reconstructing protein structures from cryo-EM density maps: recent advances and future directions](https://mlsanity.com/paper/2209.08171/) (2022)
- [Topological Obstructions and How to Avoid Them](https://mlsanity.com/paper/2312.07529/) (2023)

## Built on by (most cited first, 1 of 1)

- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)

## Abstract (arXiv)

Cryo-EM is a vital technique for determining 3D structure of biological molecules such as proteins and viruses. The cryo-EM reconstruction problem is challenging due to the high noise levels, the missing poses of particles, and the computational demands of processing large datasets. A promising solution to these challenges lies in the use of amortized inference methods, which have shown particular efficacy in pose estimation for large datasets. However, these methods also encounter convergence issues, often necessitating sophisticated initialization strategies or engineered solutions for effective convergence. Building upon the existing cryoAI pipeline, which employs a symmetric loss function to address convergence problems, this work explores the emergence and persistence of these issues within the pipeline. Additionally, we explore the impact of equivariant amortized inference on enhancing convergence. Our investigations reveal that, when applied to simulated data, a pipeline incorporating an equivariant encoder not only converges faster and more frequently than the standard approach but also demonstrates superior performance in terms of pose estimation accuracy and the resolution of the reconstructed volume. Notably, D4-equivariant encoders make the symmetric loss superfluous and, therefore, allow for a more efficient reconstruction pipeline.